While a chemically powered trip to Mars is feasible given the ability to lift a lot of mass so orbit, See SpaceX-Elon Musk, this is probably not the solution you would go for first. I think it makes sense as part of the Vision Setting that Musk does but the preference has always been for nuclear propulsion it enables faster (safer) trips and makes reusability even more effective since the ‘shuttles’ are not spending many months in transit each way.
Posit a Freighter something like the illustration below. Departing Mars having dropped of say 2, 3, 4 starships’ worth of cargo. MarsStarships shuttle up and down and provide point to point transport on Mars. EarthStarships shuttle cargo up to earth orbit. Maybe LunarStarships shuttle fuel from production stations on the Moon to reduce the cost of fuel for the starships and the Freighter.
Now you have a system that provides Access to the solar system with significant cargos and the ability to establish and support exploration stations wherever you go.